References
[1] T. Abrahamsen, V. Lima, and O. Nygaard, Remarks on diameter 2 properties, J.Conv. Anal. 20 (2013), 439–452.

[2] T. A. Abrahamsen, J. Langemets, and V. Lima, Almost square Banach spaces, J.Math. Anal. Appl. 434 (2016), No. 2, 1549–1565. CrossRef

[3] M. D. Acosta, J. Becerra Guerrero, and G. López-Pérez, Stability results of diametertwo properties, J. Conv. Anal. 22 (2015), No. 1, 1–17.

[4] J. Becerra Guerrero and G. López-Pérez, Relatively weakly open subsets of the unitball in function spaces, J. Math. Anal. Appl. 315 (2006), 544–554. CrossRef

[5] J. Becerra Guerrero, G. López-Pérez, and A. Rueda Zoca, Octahedral norms andconvex combination of slices in Banach spaces, J. Funct. Anal. 266 (2014), No. 4,2424–2435. CrossRef

[6] J. Becerra Guerrero, G. López-Pérez, and A. Rueda Zoca, Big slices versus bigrelatively weakly open subsets in Banach spaces, J. Math. Anal. Appl. 428 (2015),855–865. CrossRef

[7] J. Becerra Guerrero, G. López-Pérez, and A. Rueda Zoca, Octahedral norms inspaces of operators, J. Math. Anal. Appl. 427 (2015), 171–184. CrossRef

[8] J. Becerra Guerrero, G. López-Pérez, and A. Rueda Zoca, Some results on almostsquare Banach spaces, J. Math. Anal. Appl. 438 (2016), No. 2, 1030–1040. CrossRef

[9] K. Boyko, V. Kadets, M. Martı́n, and D. Werner, Numerical index of Banach spacesand duality, Math. Proc. Cambridge Philos. Soc. 142 (2007), No. 1, 93–102. CrossRef

[10] K. Boyko, V. Kadets, M. Martı́n, and J. Merı́, Properties of lush spaces and applications to Banach spaces with numerical index one, Studia Math. 190 (2009),117–133. CrossRef

[11] R. Deville, G. Godefroy, and V. Zizler, Smoothness and Renormings in BanachSpaces, Longman Scientific & Technical, Harlow, Pitman Monographs and Surveysin Pure and Applied Mathematics 64, 1993.

[12] G. Godefroy, Metric characterization of first Baire class linear forms and octahedralnorms, Studia Math. 95 (1989), No. 1, 1–15. CrossRef

[13] R. Haller and J. Langemets, Two remarks on diameter 2 properties, Proc. EstonianAcad. Sci. 63 (2014), No. 1, 2–7. CrossRef

[14] R. Haller and J. Langemets, Geometry of Banach spaces with an octahedral norm,Acta Comment. Univ. Tartuensis Math. 18 (2014), No. 1, 125-133. CrossRef

[15] R. Haller, J. Langemets, and M. Põldvere, On duality of diameter 2 properties, J.Conv. Anal. 22 (2015), No. 2, 465–483. CrossRef

[16] R. Haller, J. Langemets, and M. Põldvere, Rough norms in spaces of operators,Math. Nachr. (2017), 11p. CrossRef

[17] J.-D. Hardtke, Some remarks on generalised lush spaces, Studia Math. 231 (2015),No. 1, 29–44. CrossRef

[18] V.M. Kadets, R.V. Shvidkoy, G G. Sirotkin, and D. Werner, Banach spaces withthe Daugavet property, Trans. Amer. Math. Soc. 352 (2000), No. 2, 855–873. CrossRef

[19] V. Kadets, M. Martı́n, J. Merı́, and A. Pérez, Spear operators between Banachspaces, Springer, Cham, Lecture Notes in Mathematics 2205, 2018. CrossRef

[20] R. Khalil, The Daugavet equation in vector-valued function spaces, Panam. Math.J. 6 (1996), No. 3, 51–53.

[21] D. Kubiak, Some geometric properties of the Cesàro function spaces, J. ConvexAnal. 21 (2014), No. 1, 189–200.

[22] J. Langemets, V. Lima, and A. Rueda Zoca, Almost square and octahedral norms intensor products of Banach spaces, preprint, https://arxiv.org/abs/1602.07090.

[23] J. Langemets, V. Lima, and A. Rueda Zoca, Octahedral norms in tensor productsof Banach spaces, preprint, https://arxiv.org/abs/1609.02062.

[24] H. J. Lee, M. Martı́n, and J. Merı́, Polynomial numerical indices of Banach spaceswith absolute norms, Linear Algebra and its Applications 435 (2011), 400–408. CrossRef

[25] P.K. Lin, Köthe–Bochner function spaces, Birkhäuser, Boston-Basel-Berlin, 2004. CrossRef

[26] G. López-Pérez, The big slice phenomena in M -embedded and L-embedded spaces,Proc. Amer. Math. Soc. 134 (2005), 273–282.

[27] M. Martı́n and R. Payá, Numerical index of vector-valued function spaces, StudiaMath. 142 (2000), 269–280. CrossRef

[28] M. Martı́n and A. R. Villena, Numerical index and Daugavet property for L∞ (µ, X),Proc. Edinburgh Math. Soc. 46 (2003), 415–420. CrossRef

[29] M. Martı́n and T. Oikhberg, An alternative Daugavet property, J. Math. Anal.Appl. 294 (2004), No. 1, 158–180. CrossRef

[30] D. Tan, X. Huang, and R. Liu, Generalized-lush spaces and the Mazur-Ulam property, Studia Math. 219 (2013), No. 2, 139–153. CrossRef

[31] D. Werner, Recent progress on the Daugavet property, Irish Math. Soc. Bulletin 46(2001), 77–97.

[32] P. Wojtaszczyk, Some remarks on the Daugavet equation, Proc. Amer. Math. Soc.115 (1992), No. 4, 1047–1052. CrossRef